In every Locked Room Mystery, the detective can't solve the crime just by examining the relevant evidence. They always need some external inspiration (apparently) completely unrelated to everything, something along the lines of:

Sharona: Oh well, looks like you don't solve the crime. Whatever. Let's go get milkshakes. Monk: Milkshakes... The killer is lactose intolerant. So is the victim's ex-wife! Of course!!

...or...

Bob: No tea please. Dave:That's how that letter found its way twenty miles to a dead man in Sudbury!

This will lead directly to The Summation, unless there's an Evidence Scavenger Hunt in between. Often the character having the epiphany will tell the person whose offhand remark inspired it that they're "a genius" or the like; the remarker will then variously nod in a befuddled manner, ask "I'm what?", or simply demand an explanation.

Named for perhaps the most famous non-detective related example, Archimedes' exclamation of "Eureka!" after jumping into a bath and realizing that held the key to the problem he was trying to solve. (See below for details.)

The Eureka Moment shows up a lot on diagnosis-mystery medical shows, such as House, in which he does it in nearly every episode, and in the first episode of Grey's Anatomy, which isn't even a medical detective show! It may also show up on telenovelas or soap operas with some ongoing secret that defines a character or even the main plot. The truth is often almost revealed several times, by easily overheard conversations or weak evidences, and each time the status quo is kept with some contrived explanation. When the Eureka Moment takes place, The Reveal is not the result of a confession or an evidence that is too solid to be ignored, but instead the result of the hero putting all the small hints together and figuring out the truth by himself. In this case, expect a wave of several flashbacks of those hints before the "Eureka!".

Not to be confused with a Bat Deduction. While both can initially appear almost identical, a Eureka Moment leads to a coherent chain of reasoning that the detective can explain to the bystanders later; whereas a Bat Deduction, if it gets explained at all, makes even less sense after the explanation. However, although logically sound, the Eureka Moment may be enough to convince the one who came to it, but not to convince others (specially a court of law). In this case, the character may began a quest to obtain a Smoking Gun to prove things beyond any reasonable doubt.

Often used as a Deus ex Machina, albeit one that is acceptable more often than annoying. If the detective actually takes the idea literally rather than uses it as an inspiration, that is I Was Just Joking.

Examples:

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A commercial for Shell gasoline shows a scientist trying to figure out how to explore for petroleum reserves underwater without building multiple derricks and drilling dozens of holes. While at a restaurant with his son, his son uses a bendy-straw upside down to suck up the last bits of milkshake at the very bottom of the glass, causing an epiphany. Cue the scientist making a pitch for a "bendy-drill" design.

Breakstone's cottage cheese had two:

One has Paul Breakstone sitting in a bathtub while wondering how to make his cottage cheese more practical. Meanwhile, his wife is yelling at him that his bath time is over. Just before the commercial ends, his wife walks by and says "Get out of that tub!" He then gets the idea to package the cottage cheese in individual cups.

Anther has him sitting under a peach tree, wondering what he can put in his cheese so kids would eat it. "Maybe something sweet," he says, as peaches start to fall around him. Then he exclaims, "I've got it! Pineapple!" (He may have Failed a Spot Check there, but completed product has both peach and pineapple varieties.)

In an 80s commercial for Lucky Charms, Lucky was pondering what new marshmallow shape to add to his cereal, when an angry purple horse kicked him in the butt; he quickly thought of Purple Horseshoes. ("Eh, the idea just hit me!" he told the kids, while rubbing his behind.)

Anime & Manga

Detective Conan does this a lot. One time, he solved a murder he had been stuck on just by Ran mentioning that she had bought new pajamas for them. (To be more specific, she mentioned that said PJ's were a matched pair, leading Conan to realize that the murderer was a set of identical twins.)

Conan is a brilliant detective hiding in the body of a small child, so if he figures something out before anyone else, it's not uncommon for him to subtly lead those around him to their own Eureka Moment, rather than raising suspicions about himself by voicing his deductions directly.

There is also a certain part wherein Heiji and Conan figures out the dying message, but start, at Heiji's prompting, to subtly lead Kazuha to deciphering the dying message to make her feel better, as she was about to cry.

As well as Conan deliberately inducing Eureka moments to Kogoro due to Kogoro's It's Personal attitude after the murder of one of his old judo teammates.

Once per Episode in Vicky The Viking, Vicky and his crew of Vikings will be stuck in some terrible dilemma. Vicky will rub his nose for a bit, then inspiration for the resolution will strike.

In an episode of Cardcaptor Sakura, wherein two of her magical allies were cursed with Shapeshifter Mode Lock and could not effectively masquerade as non-magical, she had no idea how to break the spell until she was given a dead crab as a gift. She was inspired by the crab's shell which protects it "just like a shield!" and deduced that she could use her Shield card to protect her allies from the curse's outside interference long enough for them to transform.

This was also how she first defeated the Watery card. As she was at the aquarium with Yukito, she stares at his ice drink for a bit...then realizes that, since Watery is water, it can be stopped by freezing it.

In Utawarerumono (the visual novel), Hakuoro studies a strand of Mutikapa's fur in frustration, unable to explain why the creature fled the previous night when it had him and Eruruw in its grasp. Unable, that is, until Eruruw drenches him and the fur in tea and this trope ensues.

Arguably the entire point of Yakitate!! Japan, but applied to making bread. For example, one of these moments leads to the creation of Kazuma's "sushi-style" melon bread.

In Magic Kaito, another work by author Gosho Aoyama (author of the aforementioned Detective Conan), Kaito figures out how an old, poor magician got a parliamentary pen after a kidnapper claiming to be the Kaitou Kid took the Prime Minister after Aoko tells him the key to beating the boss of their video game is to defeat the king controlling him first.

Pokémon: Ash Ketchum has one of these in pretty much every Gym battle to turn it around (granted, his epiphanies don't alwaysmake the mostsense). If you see him panicking because his opponent is pulling some kind of unbeatable schtick, then snap his head up with a thousand-yard stare and say "wait, that's it!", chances are someone's about to get their ass beat.

Sometimes his companions do it too. May and Dawn get a few of these during their contest battles.

Invoked by Cameron by snapping his headband back if he's in a pinch during a Pokemon battle. It doesn't always work though.

Togusa gets two of these moments, early in the first season of Ghost in the Shell: Stand Alone Complex, and in both of them, he's in a bathroom, looking at the mirror. In the second, the mirror is crucial: He realizes that, from the batch of pictures he's examining, all of them show a mirror or other reflective surface, but the camera isn't visible in any of them.

In fact, this is basically his main schtick. It's one of the reasons he's one of Section 9's most effective members; he's really good at putting the pieces together.

Occurs in PatlaborThe Movie. Our heroes are trying to find out what's causing some Humongous Mecha with a new OS to go out of control. While taking a break while the investigation seems to be leading nowhere, Noah sees a dog barking at something they can't see & mentions they can hear things humans can't, cluing Shinohara in to the fact that ultrasonic waves are the culprit.

Shinohara actually gets two of these in the film. The second comes when they learn that the evil genius who created the program had a plan to make all the robots in Tokyo to go crazy at once & are trying to figure out what could cause enough ultrasonic waves to make it happen. When a whistling tea kettle causes a nearby figurine in a glass case to shake they realize it's sympathetic vibrations in skyscrapers caused by the wind. Fortunately, it'd take a mind-bogglingly huge building & incredibly powerful winds for a city-wide disaster to occur. Unfortunately a giant factory complex has just finished construction in Tokyo Bay & a record-breaking typhoon is due to hit in three days...

Naru has these regularly in Ghost Hunt, usually due to an offhand comment from Mai.

Happens twice in Fullmetal Alchemist, within the same scene. When trying to decipher a code from Scar's brother's notes, the group takes a break to reassemble Al who is in pieces, like a puzzle. May rips the bindings of the notes and with Scar and Marcoh's help reassemble it to see the nationwide transmutation circle (which Ed and Al figured out beforehand). When trying to think there was a silver lining in this, Yoki sneezes and causes the papers to shift. They're annoyed that the papers have been 'flipped over', and Al comes to his realization that the papers needed to be turned over to see the other half of the hidden message: a second transmutation circle which can be used to reverse the effects of the first.

Vegeta gets one during the final battle against Buu in Dragon Ball Z. When Goku doesn't have the energy to push the Spirit Bomb to destroy Buu, Vegeta tries to get Mr. Satan to talk the people of Earth into giving more energy, and Mr. Satan refuses, because it would probably kill them (as they had already donated their energy to form the Spirit Bomb in the first place). Vegeta angrily points out that if it wasn't for his plan to use the Namekian Dragon Balls to wish back Earth and its people, they'd all still be dead... and then Vegeta realizes that they still have a wish left, which they use to restore Goku's energy.

Iznogoud: Do you have an idea how I could get rid of the Caliph, Wa'at Alaaf?

Wa'at Alaaf: Sir, I'd rather feed my tongue to a cat!

Iznogoud(thinking): Tongue to a cat... the cat is a predator... the tiger is also a predator... the tiger is a man-eater... the Caliph is a man... so the tiger is a Caliph-eater!

Iznogoud(loud): That's a great idea of you, organizing a tiger hunt!

Wa'at Alaaf: A tiger hunt? Me? What?

In almost every issue of The Maze Agency, some seemingly random comment or event will start the gears spinning in Gabe's head and cause him to suddenly see the solution to the current mystery.

Ultimate Spider-Man: Kong (the Dumb Muscle school bully, nothing less) remembered several things: the incident of Peter Parker with the weird spider in Oscorp, that Pete suddenly became a great basketball player, that he broke Flash's hand, that Spider-Man debuted at the wrestling club shortly after the gang visited it, that Spider-Man showed up to save the school when the Green Goblin began to attack it... and Kong suddenly realized it: Peter Parker is Spider-Man!

In one issue of Amazing Spider-Man, Reed Richards and Iron Man have literally minutes to defuse a bomb left by Doctor Octopus that would destroy New York City, while the rest of the Fantastic Four and The Avengers look on. Johnny Storm suggests that Spider-Man could come up with a "fallback plan", prompting Spider-Man to point at a clock reading nearly 2 am, saying "There's no time for me to come up with a fallback... fall back... THAT'S IT!" He then syncs the bomb's electronic timer with its main OS system's internal clock. Turns out it was the first Sunday in November, meaning the end of Daylight Savings Time, when people set their clocks back an hour or "Fall back". By syncing the bomb's timer, Spider-Man was able to extend the countdown by an hour, giving the FF and the Avengers enough time to take the bombs out to sea to explode harmlessly.

In Earth and Sky, Twilight first starts working on how to help non-pegasus ponies fly after her conversations with Pinkie and Pumpkin, but doesn't settle on the idea of using artificial wings until she sees Sweetie Belle wearing a pair as part of her Princess Celestia costume.

In A Month of Sundays, Akiko as Kamen Rider Skull makes a comment about Shotaro not knowing about justice that makes Jun solve everything regarding Damballa's Carnival of the Human Spirit act clear.

Fallen King has this. Joey and Tristan ramble about The Wizard of Oz and wanting to fly home like Dorothy, and suddenly remember Kaiba's helicopter.

Graduate Meeting Of Mutual Killing: Trial 2. The surviving characters need to find a culprit candidate besides Hikasa, the one that's already under suspicion, and the Mastermind, a former suspect. However, there's almost no evidence that could point towards anybody else. Toriumi has spent the whole trial forcing people to throw a ball around in what she said was "a way to keep hands nimble and our minds even more nimble". Then Ogata realizes the true purpose of this ruse: to find who among the survivors is left-handed, as only a left-handed person could have killed the victim the way it happened, without alerting the culprit. And how did it result? It succeeded.

Dirty Sympathy: Apollo realizes that his bracelet helps him pinpoint lies when it reacts when Klavier says he can handle Daryan but it doesn't when Apollo goads him into admitting that he hates Daryan and would rather be with Apollo.

In A Taste of the Good Life, Scootaloo comments that when she was out on her own she would have tried to sneak into restaurants for scraps. "Heck, I would have eaten the empty bowls if I could have." This gives Main Course the idea of making edible soup bowls out of bread rolls.

Rosario Vampire: Brightest Darkness: In Act III chapter 42, with the revelation that Fairy Tale is still active and coming to attack Yokai Academy, Tsukune remarks to Moka that Akua and Kahlua said that Fairy Tale had been destroyed. At that very moment, Moka recalls the mystery vampire agent they fought in Ashton City during Act II, and from the evidence she failed to notice before (namely the agent's fighting style, voice over the radio, knowledge of Moka, and the fact that Akua just suddenly showed up right after they left Ashton City), realizes that Akua was said vampire agent; thus, Akua and Kahlua have been working for Fairy Tale all along.

Film — Animated

In Tangled, when Rapunzel and Flynn are trapped in a dark cave filling rapidly with water and need light to see by, this exchange occurs:

Flynn: My real name is Eugene Fitzherbert. I figured someone should know.

Rapunzel: I have magic hair that glows when I sing — I HAVE MAGIC HAIR THAT GLOWS WHEN I SING!

Ralph realizes who Vanellope really is when he sees the Sugar Rush video game and discovers her picture on the console.

Vanellope gets her own when she sees Ralph hammering away at a seemingly indestructible Jawbreaker. The second she mentions it's indestructible, Ralph splits it in half, and Vanellope's eyes light up.

In Toy Story 2, Buzz is trying to figure out who stole Woody with only a Vanity License Plate to go by; LZTYBRN. The other toys are dismissive of this, and Mr. Potato Head just says, "Let's leave Buzz to his toys." This makes Buzz realize that the kidnapper is the Al from Al's Toy Barn, especially when they make Etch-a-sketch do a composite of the suspect in a chicken suit (which he found out when he picked up a feather that came out of Al's trunk Buzz was chasing his car earlier)..

Ratigan (angry): "Oh, I can just see that insufferable grin on his smug face... (smiling) yes... I can just see it..."

A Bug's Life: Princess Atta thanks Flik for saving her sister Dot from the sparrow, stating it was very brave, adding that even the genuinely terrifying Hopper is terrified of birds. Which gives Flik the ingenious idea of building a bird decoy to scare off Hopper.

Princess Atta: Not every bug would face a bird. I mean, even Hopper's afraid of 'em. Flik: Yeah, well you know it was—(beat) Say that again. Princess Atta: I said, even Hopper's afraid of birds. (Flik sprints off, then sprints back to Atta and kisses her cheek)Flik: Thank you. (sprints off again)

In Pinocchio, just when Pinocchio and Gepetto think they'll never escape Monstro the whale, Gepetto says that they should forget it and start a fire to cook some fish. This gives Pinocchio the idea to start a fire that will make Monstro sneeze them out.

At the end of Monsters, Inc., Mike, realizing that in getting the Big Bad arrested they've gotten the factory closed, put hundreds of monsters out of work and made the energy crisis worse, tries to downgrade the events by saying, "But hey! At least we got a few laughs, right?" This causes Sully to make the connection that the energy produced by a child's laughter is ten times more powerful than the energy produced by their screams.

A bit earlier, Mike and Sulley try to escape from Randall and Mike says that they'll start a new life far away, shouting "Goodbye, Monsters Inc.! Goodbye, Mr. Waternoose!". This gets Sulley the idea to tell Waternoose about Randall's plot and hopefully solve the dilemma. That turned out to be a big mistake.

In Peter Pan, after Smee tells Captain Hook about how Tinker Bell got banished after she almost killed Wendy out of jealousy, Hook gets the idea to use her to reveal the location of Pan's hideout.

In Shark Tale, when Sykes finds out, much to his horror, that Oscar may not be a real shark slayer (earlier in the movie, Sykes joyfully told Lino, the head shark, to shut up), he asks Oscar if he is. Oscar admits he isn't, then realizes that the sharks don't know he's a fraud and gets the idea to keep his charade long enough to rescue Angie.

The Rugrats Movie: When Chaz & Howard notice baby footprints and wheel tracks in the woods, the adults realize the kids are in the woods, on the Reptar Wagon. When Drew angrily calls Stu out on this, it gives Stu the idea to search for the kids on his Dactar Glider.

At the end of Space Jam, Swackhammer is laying into the Mon-Stars for losing the game. Michael asks them why they take so much abuse from him and they respond that it's because Swackhammer is bigger...than they used to be. After this revelation, they send Swackhammer packing.

In The Iron Giant As Agent Kent Mansley leaves the Hughes after borrowing their phone he remarks about Hogarth's name which leads him to...

Kent Mansley: "Hogarth?" That's an embarrassing name. They might as well have called him "Zeppo" or something. What kinda sick person would name their kid "Hogar...? (stops and looks over to Hogarth's smashed B-B gun which Kent found at the power station. It reads part of Hogarth's name: Hog- Hug) "Hog Hug?" HOG HUG? HOGARTH HUGHES!!! (screeches his car to a stop)

Kung Fu Panda: Po has one of these after learning the secret ingredient to his father's secret ingredient soup. There is no secret ingredient. It's this knowledge that allows him to understand the wisdom of the Dragon Scroll.

Shifu has an earlier one; Tai Lung is coming, and Po has proven to be completely inept at learning martial arts. He then sees Po perform athletic feats in order to get some Comfort Food, and realizes that he can use this fact to train him.

Po:(Up in the ceiling, doing a perfect split to hold himself up while eating cookies) No, this? …This is just an...accident. Shifu:…There are no accidents.

Nick gets the idea to check the jam cams while innocently mentioning them in passing.

When Nick and Judy look at the traffic cam footage to find where Manchas was taken, the appearance of the timber wolves makes her realize his and Mr. Otterton's phrase "Night Howlers" was in reference to them. Subverted when it turns out they're actually flowers which can cause the apparent savage regression symptoms even in prey species, although the scene where she discovers this is also an example.

Judy has another Eureka Moment at her village when she finally learns what the Night Howlers really are.

In 101 Dalmatians II: Patch's London Adventure Patch is blue screening after his Broken Pedestal for Thunderbolt when one of his siblings references an episode of Thunderbolt's show where Thunderbolt escaped a cage like the ones they're trapped in, misidentifying the number. Patch dully corrects them before realizing that he can use his memories of the show to get out of his cage.

Film — Live Action

In Blazing Saddles, Hedley Lamarr's evil plans all come as a result of these.

Ryan, mulling over how Capt. Ramius could manage to get the rest of his crew off the sub as part of his plan to defect.

"We don't have to figure out how to get the crew off the sub. He's already done that, he would have had to. All we gotta do is figure out what he's gonna do. So how's he gonna get the crew off the sub? They have to want to get off. How do you get a crew to want to get off a submarine? How do you get a crew to want to get off a nuclear sub...."

Midshipman Blakeny: "It's a rare phasmid, sir... It's an insect that disguises itself as a stick in order to confuse its predators."

Captain Jack: (later) A nautical phasmid, Doctor... I intend to take a greater interest in the bounty of nature from now on. I had no idea that a study of nature could advance the art of naval warfare! Now to pull this predator in close and spring our trap.

The entire plot of National Treasure hinged on the protagonist's ability to solve puzzles and uncover secrets in this manner. Granted, the hint was invariably directly related to the solution ("Pass and Stow" was written on an ad for the Liberty Bell, the correct time was drawn on a famous picture of the building it was stored in, etc), far more so than typically for this trope.

The Big Bad also had a few of these, such as his realization that the reason why the word "Silence" is capitalized in a coded message is because it's a name (Ben Franklin's pen name) or when they arrive to the Liberty Bell exhibit only to realize that he's supposed to look where the bell was originally located not where it was moved 100 years later.

I, Robot features several effective examples of this trope including... "...the right man for the job...?" "...follow the bread crumbs..." "...I think my father wanted me to kill you..." etc,etc.

In Die Hard with a Vengeance, running into a band of under-aged looters alerts John McClane (Bruce Willis) that the villain's apparent plan is likely a distraction.

An unexpected source: in Godzilla vs. Biollante, a scientist works out the flaw of a recent attempt to neutralize Godzilla via Applied Phlebotinum by seeing dry ice hauled about for emergency refrigeration in the wake of the unthwarted monster attack.

In Independence Day, a scientist's father tells him to dress get up off the floor so he doesn't catch a cold, which gives him the idea to disrupt the aliens' force fields by uploading a virus into the mothership's computers in a reference to The War of the Worlds. This scene is parodied in the "Cancelled" episode of South Park. However, this parody is itself not an example of Eureka Moment, but of Bat Deduction.

In Inside Man, a chance comment a rookie cop makes to Denzel Washington's character allows him to figure out how exactly the hostage takers were able to stay ten steps ahead of the police.

A Beautiful Mind: Nash develops his theory out of his friends' fighting over a girl. THE NASH EQUILIBRIUM DOES NOT WORK THAT WAY!!

There's a more serious case later in the movie: Nash realizes he hallucinates when he realizes in all the years he's seen them, the little girl never ages.

After two weeks of poring over a cartouche in the original Stargate movie, Daniel Jackson finally figures out that the symbols aren't hieroglyphs, but star constellations when he sees a picture of Orion on a guard's newspaper and recognizes the shape as one of the symbols.

Played with in π. Mathematician Max consults with his mentor Sol about a numerical sequence he's trying to solve. Sol tells him the story about Archimedes (see below). Which leads to this exchange:

SOL: So what's the lesson? MAX: That an answer will come. SOL: No, it's the wife! You have to relax!

The revelation that the aliens reproduce quicker with fire is brought about by Orlando Jones' character dropping a lit cigarette into a petri dish, seconds after explaining how he hasn't smoked in years.

The alien's weakness to selenium is discovered by Julianne Moore taking off her jacket, revealing her periodic table of elements t-shirt.

Note that Evolution was, in fact, a pastiche of these kinds of movies.

In Real Genius, Knight's frustration at his sabotaged laser failing leads him to a freezer, where he realizes "It must be frozen..." and invents an entirely new and better laser using a frozen core.

In A Few Good Men, Tom Cruise briefly halts a brainstorming session with the rest of the defense team to look for his lucky baseball bat, which Demi Moore has innocently placed in the closet. Staring into the closet prompts a Eureka Moment that reveals an important fact about the case—the murder victim's clothes were hanging in his closet; if he had really been due to transfer to another post the next morning—as his CO has claimed—his things would have been packed, and his closet empty. Prompting the line "he really does think better with that bat."

In WarGames, during the tense final scene, when Falkin tries to access Joshua with his password and finds it's been taken out, David asks what they're going to do. Falkin says "I don't know. Do you?", then for some reason, Jennifer says "I told you not to play games with that thing". So, David thinks for a moment, then says "It's games. GAMES!", and proceeds to play games with Joshua.

In Blood Work, the detective realizes the meaning of the Code Killer's message ("903 472 568") looking at a check he wrote for his neighbor, Jasper "Buddy" No one, after someone else has pointed out that the message doesn't contain a 1.

The title characters have been racking their brains trying to figure out where the "Galaxy" is. Their only hint is that they were told it's "on Orion's Belt" by a dying aliennote this confuses the Agents because they think the alien is referencing the constellation Orion, but that "belt" has no galaxies on it. When Agent J sees Frank barking at a cat on the street, he realizes the alien meant collar: the alien had owned a cat named Orion, and the "Galaxy" is a trinket the size of a marble attached to its collar. (This is foreshadowed when the prince is eating with his countryman right before Edgar attacks, and uses words that aren't quite the right English terms.)

And it happens again later on, when the MIB are trying to figure out where the Bug might get a ship, and Jay spots the mural of the World's Fair, where they'd stashed a pair of flying saucers decades before and passed it off as an avante garde art installation.

Double Subversion in Men in Black II, where Agent J starts to decode a ridiculously complicated chain of arrows in a pizza shop which leads him nowhere, because he missed a much more obvious clue at the first arrow. However, the free-association links he found do turn out to be quite close to the actual plot.

Based on the Romance of the Three Kingdoms saga, the Chinese movie Red Cliff has Boisterous Bruiser Zhang Fei, not known for his tactical genius, but still unwittingly blurting out vital insights more than once. Towards the end of the movie, his comment on the enemy battle fleet ("those ships could give us more firewood than we'll use in our lifetime") leads to Zhou Yu's plan to set the entire fleet on fire.

As Eddie Valiant leaves a movie theater, a newsreel tells the news of how Maroon Cartoons was sold to Cloverleaf Industries, the same company that bought the Red Car trolley line and bid for ownership of Toontown. He runs back in and shouts, "That's it! That's the connection!"

He has another one following Doom's comment to the weasels about "dying laughing."

Dogma has one of these near the end; Jay tells Bethany (while trying to get it on, because the world's about to end) about a boardwalk he once took a girl to on a date. Bethany, after learning that the boardwalk has Skeeball, realizes that "John Doe Jersey," of whom her minister was sermonizing about earlier, is God, trapped in a comatose mortal body.

Hey, Jay was a prophet (or is that profit?), after all.

L: change the WorLd has one character hiding clues in math problems. L figures out the solution when accidentally given a clue.

In the Line of Fire: Clint Eastwood's character figures out the meaning of a word with seven letters after a chance remark by a character played by Joshua Malina.

Polly: Have you looked at this? There's markings on it, like a ruler. And there's a moon and a star.

Joe: "And all I ask is a tall ship, and a star to steer her by." A star. He wasn't talking about a place, he was talking about a star! Rana is a star! Ancient sailors used to navigate by using the night sky. They could determine their position by the moon and the stars. The Vikings were known to create maps for certain stars, latitude tables that required a key to decipher them. The key was called Jacob's staff. This has to be the key!

In Hot Fuzz, Nicholas Angel's suspicions are stumped by the question of how one person could be in multiple places at once. When he and Danny Butterman go visit the convenience shop, the conversation that takes place between Danny and the clerk causes Nicholas to suspect multiple killers. What's more, the shop clerk who triggered the Eureka Moment is one of the killers herself. Oops.

Major League: The Indians' manager is about to send hopelessly wild pitcher Ricky Vaughn to the minor leagues. During their conversation, the manager off-handedly mentions another pitcher who went down to the minors and had a successful career and points at his photograph. Vaughn squints in the pitcher's direction, and the manager suddenly realizes all his problems are related to poor vision.

In K-9 Dooley is growing frustrated with a case he's working. His girlfriend Tracy told him that he needed to relax, and the answer would come to him. Not much later, things are getting romantic between the two, when lo and behold, Dooley has an epiphany and must rush out the door with his four-legged sidekick.

William has one in The Name of the Rose book considering the secret of the library. Adso remembers how Salvatore said "tertius equi", which is Canis Latinicus for "The third of horse" (when he meant "the third horse"). William concludes: "the first and the seventh of the four" really means "the first and the seventh of the word four", and "four" is "quattuor" in Latin, so you have to push the letters Q and O!

They had a minor one earlier, when Adson dreamed a story similar to the "Coena Cypriani", a kind of The Bible parody. Which helps William to remember that there was a book in the library consisting of four texts, one of them a comment for the Coena Cypriani, another one the book they're looking for.

Iron Man 2 : While trying to perfect the arc reactor, Tony suddenly finds inspiration in his father's miniature model of the first Stark Expo. Of course, his dad did that quite on purpose during the video he left behind for Tony.

Howard Stark:This is the key to the future, Tony.Camera cut to the City of the FutureCamera cut to the UnisphereCamera cut to a prototype arc reactor

It seems that they did some research on the missing element. The element in question (118) does exist as "Ununoctium" though it is radioactive and only lasts for a very short time before decaying. It can only be synthesized with the help of a particle accelerator.

Happens to Tony again in The Avengers (2012), when he realizes that Loki is using Stark Tower to launch the alien invasion.

In Ghostbusters II, after the particle throwers have no effect on the slime encasing the art museum Egon figures out it's powered by all the negative emotion in the city. He starts to talk about needing a massive infusion of positive energy to shatter the shell.

Egon: We need something that everyone in this town can get behind. [looks down] We need... a symbol! Ray: Something that appeals to the best in each and every one of us. Egon: Something good. Winston: Something decent. Peter: Something pure. [close up of the Statue of Liberty image on Ecto-1A's license plate]

In The Man Who Knew Too Much, Ben McKenna follows the lead of spy Louis Bernard's dying words, "Ambrose Chappell", to search for the kidnappers of Ben's son. Ben visits a taxidermy shop owned by a man named Ambrose Chappell, only to learn that Mr. Chappell has no association with the criminals. As Ben's wife, Jo, waits anxiously for him to return to their hotel room, one of her friends, Val, asks her the name of the person Ben's searching for. Val mistakenly calls him "Church", so after Jo corrects him with the word, "Chappell", she pauses, then exclaims, "It's not a man, it's a place! It's Ambrose Chapel!" Jo's friends proceed to help her find the address of this chapel in the phone directory, before she leaves them to search there.

Crossed with Oh Crap!; In Man of Steel, Lois tells Clark that they gave her a Mind Probe and learned all her secrets. Clark replies that Zod was inside his head as well... then he connects the dots and realizes they know where he lives, probably enforced by him cocking his head slightly like he was listening.

In We're the Millers David conceives his "let's pretend to be a family" plan after seeing a police officer helping out a family in a RV.

In The Cannonball Run, J.J. and Victor debate what to drive in the race while driving around in a boat. They get into an accident and are taken to the hospital in an ambulance. J.J. asks the doctor how long it's going to take them to get to the hospital. The doctor explains that the ambulance can easily slip through traffic due to being an emergency vehicle. Guess what they end up driving in the race.

In Oz: The Great and Powerful, Oscar is starting to feel overwhelmed by the knowledge that he has to fight two witches armed with very real magic that he doesn't have, and the only thing behind him is an army of craftsmen. While tucking in the China Girl at bed time, he tells her about Thomas Edison, and that he could use his knowledge of natural science to create wonders and realizes that he can use his own knowledge of special effects and theatrics to basically bluff the witches into submission.

In Tell No One, Alexandre has received a mysterious e-mail from someone claiming to be his dead wife, Margot, who's left him a username and password to answer another e-mail that's being sent later. Alexandre can't access the account no matter how he tries, much to his frustration. That night, he's out walking the dog when he hears "With or Without You" playing, and realizes what the username and password are really *supposed* to be, allowing him to go to an Internet cafe and access the account.

In Thank You for Smoking, Nick hits upon his strategy for the congressional hearing while watching Bobby eat apple pie covered with cheese.

In Interstellar happens when Murph finds out her father is actually the "Ghost" that contacted her in her childhood and also when discovering the solution to Brand's equation. She even shouts it out of joy, throwing the papers everywhere after writing it.

In Philomena, Martin realizes that Michael was aware of — and took pride in — his Irish ancestry.

In The Spy Who Came In From the Cold the burnt-out British spy Leamas is seconds away from successfully competing an assignment to destroy an enemy agent, when stupid mistakes by his service in London destroys the entire plot, allowing the enemy agent to escape. You look into his face and you realize that the entire plan was about saving that agent who has come over to the British and killing the man who suspects him. Leamas was just a pawn.

High School Musical: A villainous example from Sharpay, when she gets an idea to make it so that Gabriela can't make it to the auditions.

Sharpay: Okay, so the decathlon and and the basketball game are on Monday, and the auditions are on Friday. Too bad, all of these events weren't happening all on the same day...'at the same time.

I am jumping up and down because at the very moment Dick Clark said the word "Go," it was like an invisible hand reached out and snatched away my veil. And for almost a minute, I understood everything. When that veil isn't hanging down right in front of a person's face, a minute is long enough to realize a lot of things.

Agatha Christie loved doing this in the Hercule Poirot novels. Very frequently, he fits the pieces together after inspiration from a chance remark by one of the other characters; to Poirot's credit, he never fails to explain precisely how it helped him break the case.

Every Cat Who... novel by Lillian Jackson Braun features Koko the Siamese doing something odd which eventually leads to Qwilleran having a Eureka Moment. How plausible Koko's behavior is, either taken at face value or with the strong hint he's trying to give clues, varies considerably.

Lampshaded in The Burglar Who Traded Ted Williams: While Bernie Rhodenbarr is talking with a friend, she mentions the Cat Who... series, when his cat suddenly launches into strange behavior and Bernie solves the crime. Subverted, in that he'd already solved the crime, but didn't care about revealing the result. When the cat acted, as if on cue, he decided to play along.

Sansa supplies her father with one when she says that Joffrey (who she has a mad crush on, the poor girl) is nothing like his father, Robert. This finally makes Eddard realize that none of Cersei's children take after Robert — though all of Robert's bastards do — and the kids are most likely the product of incest between Cersei and her brother, Jaime.

Tyrion gets one two books later, when the readers have all pretty much forgotten about the never-quite-solved mystery of who sent the assassin with the dagger to try to kill Bran from the first book, when he hears Joffrey bragging about how he's very familiar with expensive things like Valyrian steel. Because the chapter is told from Sansa's point of view, the readers only find out what's on his mind when he gets her alone for long enough to ask "Hey, do you know if Joffrey had any reason not to like your brother?

In American Gods, this is how Shadow figures out where a small-town serial killer has been hiding his victims' bodies, acting on a comment from a god who knew what was going on, and was trying to clue him onto it.

This is nearly Elijah Baley's entire modus operandi in Isaac Asimov's Robot novels. The third and final book in the series even barely gets away with justifying it.

In The Caves of Steel, Lije Baley figures out the murder mystery when his partner casually brings up Enderby's glasses. All pieces of the puzzle then come together: Lije realizes that Enderby (who was earlier established to be psychologically incapable of killing a human) accidentally murdered a person, instead of destroying their robotic lookalike, because he couldn't see clearly when his glasses shattered.

In The Naked Sun, he asks Daneel to "give him a hand". The robot responds by looking at his hand as if he was supposed to actually give it to him, leading Elijah to realize that the murder weapon was a robot's detachable arm.

Asimov also wrote an essay about how this sort of thought process works called "the Eureka effect". It's even made it into a few high school literature books.

An extremely complicated version of this trope is pretty much the premise of Chasing Vermeer.

Timothy Zahn likes this trope. Or, more accurately, this trope fits his style. Many of Zahn's original works are First-Person Smartass, and the settings are similar to Hitchcock-style suspense/intrigue mysteries, so there's guaranteed to be one when the protagonist finally puts the pieces together. (Though the reader, unless he figures it out too—which is sometimes possible and sometimes not—won't know until The Summation.) Some examples:

The Icarus Hunt has at least two: One when a comment makes the protagonist realize another person's murder was connected with something completely different than he'd been assuming; another when a different comment triggers a flashback. The Summation indicates he may have had another couple more along the way that the audience wasn't even privy to.

The Quadrail Series tends to have one per book, minimum; most notably, the moment in Night Train to Rigel when Compton figures out how the FTL trains work.

This even shows up in his Star Wars Expanded Universe work, though those get more promptly revealed to the reader: in Survivor's Quest, a random comment by Luke triggers a flashback for Mara, in which she recognizes a major inconsistency in some of their companions' back story.

And finally, one for Leia in The Last Command. Talon Karrde mentions how he was a Chimaera prisoner, and for Leia, "suddenly, all the pieces had fallen into place...and the picture they formed was one of potential disaster."

Aside from the few times they recognize the answer instantly, the characters in The Da Vinci Code seem to rely solely on this trope to solve all the various puzzles and sub-puzzles. For the last puzzle before the book's climax, we don't actually get to see the main character work out the answer.

We don't get to see it, but we do get the lead in. The answer to the last puzzle is a word: apple, and the last thing Langdon happens to look at before his off-screen Eureka Moment is an apple tree.

Nero Wolfe does this quite a bit. He's got all the pieces, but can't make them fit together, Archie (or one of the suspects) says something that causes him to look at one particular thing in a different way, and everything falls into place. He will often admit to Archie when it was something that he said or did; if it was someone else, he saves the information for the Parlor Scene. Both Archie and the reader know one has just occurred when Nero starts doing his "lip exercises".

Subverted, while lampshading the subversion, in Mil Millington's "Love And Other Near-Death Experiences", in which the central character has a startling realization that he recognizes would qualify as a Eureka Moment — except that nobody did or said anything to trigger it, it just happened without prompting.

In Harry Potterand the Half-Blood Prince, a sarcastic comment by Harry ("Fifty-seventh time lucky?") about his inability to get a crucial memory of Voldemort from Slughorn inspires Ron to suggest Harry use his luck potion, which proves effective. A similar scene occurs in the movie, only (in keeping with the screenwriter's general inclinations) reversed: Ron's comment inspires Harry.

In Deathly Hallows, we're treated to Harry's entire train of thought as a broken talking stone gargoyle triggers his memories and he realizes exactly where the last Horcrux is hidden.

In Memory, Sorrow and Thorn, near the climax of the third novel, Binabik the troll has a classic Eureka Moment during his party's escape from the Norns beneath Asu'a, as a result of an offhand comment from the dwarrows who are aiding them. Unconventionally, this leads not to the solution to the plot but the horrifying realization that the heroes have been doing the Big Bad's bidding the entire time.

In the grand tradition of mystery novels, happens frequently in Ngaio Marsh's Inspector Alleyn series. An interesting departure is that the Eureka moment for Alleyn usually occurs near the middle of the book, with the reader catching up as more evidence is gathered.

Played straight at the end of the book, when remarks of Detritus and Fred Colon make Vimes realize the Big Bad had been rubbing the hints of his plot in Vimes' face, assuming Vimes wouldn't get them.

Lampshaded in that "eureka" is a Ephebian word meaning "Bring me a towel". And in fact, we learn this is a regular occurrence for Ephebian philosophers, to the point that nearby stores keep a large supply of soap, towels and bath salts.

Subverted in Reaper Man; Inventor Ned Simnel is trying to think up a way for his combination harvester to move without a horse when a blast of steam goes off. Ned just gets annoyed on how he's always getting interrupted when trying to think. According to The Discworld Companion, this has happened over a 150 times.

Subverted in Moving Pictures. CMOT Dibbler has been selling advertising space in some pictures, but is told to stop. Then he hears about a mistake someone made while editing a film, leaving in a frame which was just a picture of gold. Nobody noticed, but everyone was thinking about gold when they left the theater. It looks like he's about to figure out a way to sell advertising after all... but he puts in five minutes of film depicting what he's trying to advertise, on the reasoning that if one frame can do that, five minutes worth must work wonders.

In Dorothy L. Sayers' Whose Body?, Lord Peter Wimsey's moment of revelation is explicitly compared to staring at jumbled letters until they formed a word of their own inclination.

In Remote Man, Ned comes up with his plan to bring down Laana's smuggling operation when he's browsing in a dime store. He picks up a pin cushion that he discovers has a music box inside playing a familiar tune: The Entertainer. This brings back memories of watching The Sting with his father, which in turn sparks his plan, which is to invent a person, a rich businessman with his own fabricated website, to be a client of Laana.

Earlier, Ned overhears a conversation mentioning "an anchorman in Kingston". When he later learns that Kingston is the capital of Jamaica, he realises that what he heard was "a nanka-man", nanka being a local term for the Jamaican Boa.

In Heroes Die, Toa-Sytell has one when he reads the Monastic records on Caine and realises that he's an Aktir.

In Anno Dracula, Genevieve and Charles are struggling with their investigation into Jack the Ripper's murders. Genevieve wishes aloud that Dr. Seward were with them, as he treated all the victims and could have told them what they had in common. As soon as she says this, Charles realises something; They had Seward in common. Jack Seward.

Happens quite a bit in The Dresden Files. Most recently, in Cold Days, Harry was talking with someone about his daughter and how much he would give to not have her hurt from any source, which makes him pause. Seconds later, he unravels a plot that's been in play for eight books.

In I Want My Hat Back, the Bear, after a long and fruitless search for his hat is asked to describe it: "It's red and pointy and... I HAVE SEEN MY HAT!"

In Astrid Lindgren's Emil of Lönneberga books, there is a part where a man buys an unshod horse. All attempts to shoe it fail due to the horse kicking, and one man remarks that the buyer was cheated — at home, they tried to shoe it twenty times. Angry, the trader says anyone can have the horse for free, but when Emil takes him up on the offer, says he'll need to get him shod first. However, the horse's reaction reminded Emil (a five years old) of his family's servant, and he realized that the horse was merely ''ticklish''. So, he manages by holding the horse's hoofs, which have no nerves by definition. The trader tries to back out of the deal, but the crowd forces him to keep his word.

Ellery Queen is prone to these. For example, in The Scarlet Letters he is watching some wet paint run in the rain when the meaning the victim's Dying Clue suddenly becomes apparent to him.

“The crime isn't murder,” Miles whispered, his eyes widening. “The crime is kidnapping.” The murders had come subsequently, in an increasingly panicked cascade, ... “My lord, are you all right—?” Ekaterin's voice, in a fierce whisper: “No, don't interrupt him. He's thinking. He just makes those funny leaking noises when he's thinking.”

T*A*C*K: Often, just before "turn the page for the solution". Another character will usually make a reference to something vaguely related that will trigger a "I just figured out the answer!". It's usually Toria who triggers Will, but occasionally other characters will trigger Will or Toria into figuring things out.

Live Action TV

In Angel this is lampshaded when Angel announces that they're waiting for Wesley's Eureka Moment — at which point Wesley promptly shouts "Eureka!"

Angel: "Listen, listen, listen... What are you listening for?" Fred: "The click. When it all comes together and makes sense. There's like a click in your brain and then you understand things again."

The Dutch Detective show Baantjer featured, in each and every episode, a Eureka moment when the protagonists were in their usual bar, when the barman makes an offhand remark. The Euraka moment always looks and sounds the same too. Eventually Lampshaded, when the barman asks if he doesn't deserve be put on the police payroll.

This trope was regularly parodied in the 1960s Batman TV show. "That's it, Robin! The man in the grey suit was whistling the Star-Spangled Banner BACKWARDS! The Joker's lair must be in the old fireworks factory! To the Batmobile!"

Battlestar Galactica ("Scattered"). Gaeta comes up with the idea to network Galactica's computers by lining up soap bars in the latrine.

In the pilot episode of Bones, Brennan is sitting down to have a drink and discussing a book written by the episode's original patsy, when they come across the patron saint of fish, and Brennan realizes who the real baddie was, based on the fact that he kept tropical fish tanks that used a certain type of diatomaceous earth, and runs off to take him down by herself.

The episode "The Maiden in the Mushrooms" has a C-plot involving Hodgins using the last of Finn's late grandmother's special hot sauce and trying to recreate the recipe using the lab equipment to analyze its contents. He succeeds and Finn starts digging into the catfish that's just like his grandmother used to make, and Hodgins tells him to slow down or he'll choke on a bone. Finn says that that's not a worry with a baby catfish because their bones are too malleable. Cue realization that the victim was young enough that hanging wouldn't necessarily have snapped her hyoid bone.

The midseason finale of the final season of Breaking Bad ends with Hank realising his brother-in-law Walt was Heisenberg all along. On a toilet.

Castle is beginning to show an aptitude for Eureka Moments, usually inspired by his daughter. In a reversal, he gave one to his daughter in one episode.

Castle and Beckett will often have these moments simultaneously (or near simultaneously) in order to demonstrate how they click (in more ways than one). For one example, Beckett was writing something on The Big Board when she suddenly had a brainwave... and Castle at the exact same time ran in from the elevator, having obviously had the exact same brainwave.

Charmed: In the episode "Y Tu Mummy Tambien," after Phoebe is kidnapped by Villain of the Week Jeric, Piper and Paige turn to Cole for help only to find him holed up and trying to find a way to kill himself. Piper suggests he take therapy, to which Cole retorts that he'd "rather chop his head off than have it examined"... which gives him the idea to summon a guillotine and do just that. He never gets to actually use it, however, as he decides to team up with Jeric afterwards.

Happens with astonishing regularity in The Closer. Brenda has them all the time... in fact, she had one when she was at her father's hospital bed, and another when she was trying on her wedding gown.

Frequently used in Columbo where the detective would see something that would inspire him and would only be revealed at the end, once that critical detail had been used to lure the killer into revealing their crime unwittingly.

In the episode "Compulsion", Gideon has a friendly conversation with a student who broke up with his girlfriend for another guy. The student says that his ex told him he would suffer the wrath of God, leading to the conclusion that the episode's unsub is religiously motivated.

And in a later episode, Reid figures out how to get back a lost childhood memory while having a chat with a hooker in front of an automatic poker machine.

Girl: So, did it work? Did she quit smoking? Because I've tried everything. The patch, pills...

Reid: You should try hypnosis. They've had great results with... hmm. [Gets up and walks away.]

Girl: Hey, wait, you won, like, two thousand dollars on this machine!

Reid: (distracted) Keep it.

Morgan: You do realize that you just gave two thousand dollars to a hooker, right? What were you talking about, anyway?

Reid: How to quit smoking.

Later seasons of CSI have relied heavily on episodes in which evidence gathered for one case provides the Eureka Moment for one or more of the other cases in the episode.

In a CSI: NY episode, Hawkes watches a Jennifer Lopez video during his lunch break. While admiring her, um, assets, he remembers they are insured, helping him figure out the case — it's an insurance scam.

This is a staple of Death in Paradise. Towards the end of each episode, the investigation will have hit a brick wall until a seemingly innocuous object or statement from one of the others will prompt this in our British protagonist. Usually, this results in confusion from the rest of team, especially in Season 3 as Goodman tends to talk to himself while making the connection and prompting Dwayne to comment that Goodman is crazy.

Doctor Who has it happen so many times, it's practically a drinking game at show marathons.

The Talons of Weng-Chiang makes fun of the word itself: the Doctor claims that it translates from Greek as "This bath is too hot."

In Time Heist, in Karabraxos' vault, the Doctor figures out who the Architect is. As befits his Large Ham style, he strikes a nearby gong just to accentuate the moment.

Doctor: I hate the Architect.

This is also a Once per Episode occurrence on the 1975-6 Ellery Queen TV series. In the final act Ellery will be in some mundane activity, usually with his police Inspector father, say "Of course!" and break the fourth wall to ask the audience if they've solved the mystery.

Sheriff Carter solves problems with literal Eureka Moments, followed by saving the town with an It's Up to You sequence. (Especially ironic since he's the supposedly only normal person in a town full of geniuses.) Sometimes, however, the Eureka Moment moments come from the geniuses after the sheriff suggests a Muggle solution.

Inverted in Everybody Loves Raymond, when Ray lies that he has a great Christmas present ready for Debra, which he got the idea for on a trip they took to Manhattan a while back when she shouted "Oh my god!". On his brother's advice he gets her a First Edition copy of To Kill a Mockingbird, then has to blunder his way through an explanation of what she shouted "Oh my god" at in Manhattan that caused him to think of the book.

In Farscape: Not so much a mystery as a scientific puzzle, but while John tries to figure out how to save Earth from the Scarrans at the end of the regular series, Aeryn tells him not to beat himself up over it. Because of the way she phrased it, he gets an idea for a solution, kisses her, tells her to "Never change!", and runs out. Aeryn gets a half-pleased, half-bemused look on her face.

In Fringe, due to Walter Bishop's mental fogginess, he frequently has difficulty remembering certain things. He frequently paces around and mumbles various mnemonics and unintelligible fragments of an idea until someone, often Astrid Farnsworth, happens to say something that jogs his memory.

Spoofed in Garth Marenghis Darkplace ("The Apes of Wrath") when people start devolving into monkeys due to contaminated water. The hero suddenly puts all the pieces together (the fact that his friends turned into monkeys after drinking a cup of water, the only two people who haven't turned into monkeys aren't drinking the water, and that the water's a sickly green color) and concludes... that he's thirsty.

The heroine of Ghost Whisperer seems to have moments like this now and then when trying to figure out the identity of the Ghost of the Week.

On Good Eats, Alton was agonizing on what to do for an avocado-themed episode (while his assistants are suggesting varieties of guacamole) when one rolls into a sink full of water. He shouts "Eureka!" when he sees that the avocado floats.

Gotham: In "All Happy Families Are Alike", Bruce and Alfred tear Thomas Wayne's study apart looking for some clue as to what he had been secretly working on. After failing to find anything, Alfred attempts to persuade Bruce that he is on a wild good chase and remarks "There are none so blind...". This suddenly gives Bruce the inspiration for where he should be looking.

All the characters of Graduados, except the seniors and the teenagers, attended high school together in the eighties, and they are now in their forties. Unknown to them, Patricia Longo is Jimena Benitez, the fat girl of the class that everybody insulted and mocked. She got thin, she changed her name... and wants revenge. Several hints of her true identity were released here and there. And one day... a comment from Patricia left Loli pondering. She had a wave of flashbacks in the night, and got her Eureka Moment: Patricia is Jimena!

Hogan's Heroes: Colonel Hogan gets most of his ideas this way. A typical scenario involves pacing while the others discuss a problem. He then pauses, smiles, and says "Wait a minute," before outlining the plan.

In Homeland, Carrie has one when watching some musicians play at a bar and realising that Brody doing the same might be a signal.

House does this every episode, most of the time inspired by Dr. Wilson. It's actually stated on the show that House will seek out Wilson to talk about unrelated subjects because it helps to jog his mind and inspire Eureka Moments.

Wilson: Who the hell chats about their blood type? You had to have tested me. House: (to himself) There's no reason to ask anyone their blood type... (House pauses, and as usual starts staring into space as if he's working something out in his head) Wilson: You're about to run out of here now, aren't you? (House gets up and leaves immediately)

Or, in another episode:

Wilson: ...and you aren't even listening to me anymore, because I just gave you the solution to your case, right? And now you are going to leave without saying anything else. House: (as he leaves Wilson's office) No.

House once actually showed up outside Wilson's apartment after they'd had a falling out in the hope that if he could get Wilson talking long enough, he'd eventually say something that would give him an epiphany. It didn't work.

Wilson had one once as a result of noticing an obscure detail about a patient. He referred to it as a "House Moment."

Taub had one in an 8th season episode while being chewed out by House for not being objective about a patient. He said "... I think I just had a light bulb." House immediately stopped ragging on him and said "You can trust light bulbs."

Amber: Thank you! Wait, why are we geniuses?explanation Victor is their main enemy for this season and Corbierre is his "pride and joy"

Done frequently in Inspector Morse with a inconsequential remark by Sergeant Lewis providing the inspiration for Morse to solve the mystery. In an ITV 3 trailer for Sequel SeriesLewis, Inspector Lewis actually refers to "that eureka moment".

Jonathan Creek actually used this so much that at one stage another character actually anticipated that a totally random object would trigger a Eureka Moment in Jonathan, and so caused a distraction.

Played with in an episode of Kate And Allie; Kate's daughter Emma receives an ugly Aztec statue from her dad for a birthday gift, only to have various people trying to buy the statue from her or threaten her if she doesn't give it up, without explaining why they wanted the statue. At one point, Allie finally shouts, "Just take the money, Emma! The way they're chasing after it you'd think it was The Maltese Falcon!" With that clue Emma realizes that the statue must contain something valuable and breaks it with a rolling pin, revealing that the statue contained a ruby pendant and a note from Emma's dad. It turns out that the "interested parties" were friends of Emma's dad, who staged a mystery for Emma to solve, and that Allie was in on it from the beginning.

Classic example, from M*A*S*H; Hawkeye and BJ challenge Winchester to join them in a poker game with Col. Potter, Major Houlihan, Father Mulcahey and Radar, only to have Winchester way ahead halfway through. While Winchester is taking a break, the others complain about his annoying whistling, with Radar commenting that he keeps whistling even louder when he's bluffing. A few seconds later...

Hawkeye: A-ha! He whistles louder...

All: ...When he's bluffing!

A staple on Midsomer Murders, where DCI Barnaby regularly receives the inspiration for solving the murder case from unrelated conversations, often in chats with his wife about whatever happens to be their personal side story (preparations for a county fair, talking with a real estate agent, etc.) in the episode. In one case, he was at his daughter's big play, when the moment came from one of the actor's lines. Cully goes onstage just in time to see her dad running towards the exit, knowing exactly what's happening.

Monk: In one episode, the date on a ketchup bottle let him work out a whole case he hadn't even known existed! In earlier seasons, this frequently led to some humorous non-sequiturs, such as "If he's 37 years old, then I know how the judge was killed."

A common occurrence with William Murdoch in Murdoch Mysteries. Lampshaded in "Convalescence" when Crabtree is standing for Murdoch as acting detective. Having reached a seeming dead end in the case, Crabtree starts staring The Big Board. When Higgins asks he what he is doing, Crabtree says that whenever this happens to Murdoch, he stares at the board and everything suddenly falls into place. He then adds that it is not as easy as Murdoch makes it look and all he is getting is a headache.

In "The Kissing Bandit", Julia Ogden's sister is trying to explain to Murdoch that, even though Julia has settled for marrying someone else, that doesn't mean she doesn't love Murdoch, if he would only act on his own feelings, rather than resign himself to the situation. She then uses the reaction of a woman kissed by the Bandit as an example of being swept away by one's feelings.

Murdoch: I wasn't aware I had resigned myself to anything, Miss Ogden. But you have given me some insight into this case.

Ruby Ogden: I have? I didn't intend to.

In NCIS, McGee got one while taking a polygraph test when the examiner mentioned that the regulars on her morning train were worried when they didn't see her.

Happens in nearly every episode of NUMB3RS, with camera effects indicating the mathematical wheels turning in Charlie's head. Usually followed up with the strangely PBS-like explanation of the relevant analogy.

Padre Coraje has a Non-Powered Costumed Hero, Coraje, who poses as the priest of the village. Clara Guerrico remembered several details about both of them, and realized his secret identity.

In the Parks and Recreation episode "Eagleton", Leslie is struggling to overcome her rival Lindsay in the neighboring town, who put up a fence in the middle of a shared public park. Ann offers to beat Lindsay with a baseball bat, which gives Leslie an idea. Cut to a few days later, when Leslie has turned Pawnee's side of the park into a baseball field using the fence as a convenient boundary.

In the Power Rangers in Space episode "Five of a Kind", T.J.'s watching video footage of the Rangers' last fight against The Psycho Rangers (who the Rangers have struggled badly against up to this point, as each Psycho copies their individual fighting style) when the color disappears from the video. The monochrome footage gives him the idea to disguise the entire team in the same color uniform, so the Psychos won't know who is who.

In Prison Break, Mahone puzzles over a clue to where Michael is going that ends with the word "woods." After seeing the badge of a cop whose last name is Rivers, he realizes that the clue does not refer to a place but a person.

Shawn Spencer in Psych frequently has major Eureka Moments very early in the episode. Usually he's figured out the particularly far-fetched explanation very early (such as figuring out that a victim had been bitten by a T-Rex... don't ask), but the whole episode then revolves around him and Gus trying to find the evidence to prove the outlandish theory correct. Reverse Detective Work, maybe?

Sam induces one in a doctor in the pilot episode of Quantum Leap. When the leapee's pregnant wife goes into early labor, Sam uses his medical training to recommend certain drugs to stop the labor. Unfortunately, these drugs do not exist in 1956, leading an air force physician to assume that he is pulling a stunt. Sam then remembers that the technique (developed in the 1960s) originally used alcohol; when he tells the increasingly irate doctor to think about what an intravenous solution of 5% alcohol and glucose would do, the doctor considers the implications and then realises that the idea is sound.

This trope regularly occurred on Remington Steele, with Steele being reminded of an old movie which somehow resembles the case he is working on. Sometimes used as a Red Herring when Steele's movie references end up providing a plausible but entirely incorrect solution.

In one episode of Seven Days, a scientist discovers a cure for cancer by seeing some water on her morning jog. The discovery is apparently averted when Frank goes back and interrupts her right before she sees the water — but she discovers it anyway after receiving a similar Eureka Moment from some coffee Frank gives her.

Scrubs uses this regularly as well. JD often sees his friends solve their problem of the week and realizes this can be applied to his own situation.

A memorable example; in the third season episode "The Sign of Three", during a long, rambling (and surprisingly touching) best man's toast at John Watson's wedding, he mentioned a case that he was not yet able to solve, highlighting how John had helped save the life of the intended murder victim, an Army officer. At the end of the speech, when he called for a toast for "John Hamish Watson", he realized that a woman involved in another case knew John's Embarrassing Middle Name and that he was getting married, and followed that thread to uncover that one of the guests at the wedding, John's old army commander, was a target for the same attempted killer. He decides to tell John about it, and than Sherlock, John and Mary solve the case together, and John's old Army commander doesn't get killed.

Hong Kong prime time dramas seems to love this trope. Case in point, the period drama Song Shijie, where the eponymous character is a court lawyer who seems to be surrounded by people and incidents that randomly give him pivotal clues.

A simultaneous example occurs in the Square One TV Mathnet mystery "The Case of the Mystery Weekend". While playing a game of color 8-ball, where the player must sink balls in the order red-orange-yellow-green-blue-purple-black, George Frankly realizes that guests have been disappearing in a similar order, going by the decorations of the rooms they were assigned. Later, fellow guest and sax player Miles Reed reveals he deduced the same thing, presumably inspired by "Somewhere Over the Rainbow", the song Reed had been practicing throughout the weekend.

Stargate SG-1. If Jack O'Neill is going to solve the episode's problem without shooting his gun a bunch, he'll say something random and Carter'll build a solution out of it.

When Anubis attacks Earth with a weapon that will cause the Stargate to explode, everyone is desperately trying to find a way to stop the process. Until alien visitor Jonas Quinn notes that the Stargate is much bigger than the doors to the gate room, and asks how they got it in. (Turns out the ceiling opens.) This brings about the sudden realization that they don't have to shut down Anubis's weapon, they just have to get the Stargate off the planet and let it explode somewhere else.

Another one later in the same episode when, after O'Neill is unable to get the Stargate to a safe altitude with the X-302, he realizes that for these purposes the unstable hyperdrive is just as good as a fully functional one: it doesn't matter where the gate is sent, so long as it's not here. This hadn't even been considered as a backup plan; it just suddenly occurred to O'Neill when he ran out of fuel before reaching escape velocity.

In the Star Trek: The Original Series episode "Court Martial", Kirk idly mentions to Spock that he might be able to beat his next captain in chess when it seems that the evidence against Kirk seems airtight and he might be punished for seemingly killing a crewmember. Spock utters "Chess..." and heads out. When McCoy finds him later, the doctor's incensed that Spock's just playing a leisurely game of chess while his best friend is in danger before Spock adds in that he just won four games in a row, an impossibility. After winning a fifth, he tells McCoy that he had been with Kirk the entire time everything had happened and that while a computer can be "flawless", something didn't add up. Winning five games in a row gave Spock the proof he needed that the computer, and thus the evidence, was tampered.

True Detective: In the first Season Finale, the protagonists try to crack the Yellow King conspiracy once and for all. Cohle says they'll need to look at the old files with fresh eyes, "like we're totally green." This reminds Marty of a child's description of her attacker as a "spaghetti monster with green ears". Digging through the files, he finds a relevant photo of a house...with a suspiciously fresh coat of green paint.

Cohle:...Fuck you, man.

UFO episode "The Dalotek Affair". Early in the episode, as part of an alien plot a meteor falls on the Moon. Late in the episode Commander Straker remembers a single word from a 10 year old TV broadcast ("fireball") and realizes that his subconscious mind is trying to tell him about the meteor's significance.

Ultraman Mebius has such a moment in episode 34, when watching Ryuu light a campfire by twirling a stick on a piece of wood allows him to develop the drill kick technique he uses to defeat the KaijuOf The Week

An episode of The West Wing has Josh struggle all episode with trying to determine a solution for an unfavorable rider to a long-fought for bill that will result in a piece of land being used for strip-mining. After wracking his brains all episode without success, a chance comment from Donna about antiquated computer systems reminds him of a long conversation with the President earlier in the episode about national parks, and he comes up with the idea of using the Antiquities Act to have the President declare the region a national park.

Josh and Donna had a few of these over the series. Another one concerned judicial nominees after the death of a Supreme Court Justice, and the declining health of the Chief Justice. Although all the characters were unhappy that they couldn't get the nominees they wanted confirmed, it wasn't until Donna told Josh the story of how her parents got their cats (they went to an animal shelter, and they couldn't decide between two, so they got both) that he has the idea of letting the Republicans name whoever they want for the open seat, if they will accept the Democratic nominee for Chief Justice.

This was one of F Troop's many Running Gags. There would be an impossible situation, such as O'Rourke's annoying Irish father visiting the fort, and overstaying his welcome. Corporal Agarn would make a comment like "He'll never leave unless the Little People show up and convince him to go back to Ireland." Someone else, realizing this was a great idea, would say "Agarn, I don't know why they say you're so dumb!" Moments later, Agarn, Wrangler Jane, and Cpt. Parmenter would be dressed as leprechauns and sneaking into the old man's bedroom. Suddenly, Agarn would say "WHO says I'm dumb?"

Radio

On Absolute Power Martin's comments (usually that they should give up, or similarly unhelpful) often give Charles a Eureka Moment. Lampshade Hanging in the second episode:

Charles: You have that ability, peculiar to the mediocre, of making the obvious statement that brings out the genius in a genius.

Casterbridge: You know, all along there's been something nagging me about this case. Something not quite right about it. And it took Sloman here to make me see it. "That's the way the cookie crumbles" he said. Clumsily and for no obvious reason.

Video Games

Parodied in the first season finale of Telltale's Sam & Max: Freelance Police series. Most fans had figured out by this point who the season villain was, so at the beginning of the episode Sam is trying to figure out who the villain is. Max has to drop increasingly obvious clues before Sam finally figures it out... through a nonsensical logical leap based on the fact that he's never said the word "morning."

The most triumphant example in the first game has to be in case 4. You're backed into a corner, you have no proof that the witness isn't who he says he is, and it looks like you're going to lose. von Karma then says something as a joke which suddenly turns everything around: "Perhaps you would like to cross-examine the parrot for some comic relief?"

This trope is probably why the Edgeworth-based spin-off game makes his Catch Phrase "Eureka!" (Though quite a few fans thought this was a little Narm-y.) He actually does get one in AAI case 2, when Zinc LeBlanc falls over the railing in the plane's cargo bay.

At several points in AAI Edgeworth will hit a brick wall with his confrontations, but then the player is reminded of past innocuous scraps of conversation, then links together half a dozen or so pieces of logic, which leads to a whole new perspective on the case. Sufficiently awesome music starts up to accompany this.

Dual Destinies features Revisualization (Thought Process in Japan), which shows the character's thought process as they come up with the Eureka Moment. Needless to say, much like everything else in the series, it's epic.

Heavy Rain: The clues start coming together in the last act for the characters (and, by extension, the player) this way.

In Assassin's Creed II, Ezio and an ally are trying to figure out how to get into the Doge's palace to prevent an assassination plot. The friend remarks that the walls are so high, "only a bird could get over them". Ezio hears this and mutters "A bird... yes...", then runs off to ask Leonardo da Vinci about that flying machine of his...

Leonardo later has his own Eureka Moment after they discover that said flying machine doesn't get very far on its own. In his frustration, he throws a piece of paper into the fire, where it starts to rise from the heat, inspiring the crew to set up bonfires across Venice.

Bartolomeo inspires Ezio to another Eureka Moment when he realizes that they have no chance of storming Baron de Valois's fortress to rescue Pantasilea. He starts wondering if it would just be best to just give himself up, leading Ezio to his idea of disguising the mercenaries as French soldiers and pretending that he surrendered himself to get past the gates.

In one ending, Junpei looks at Snake's dead body, whilst searching the Shower room for Clover, and notices his left arm's bone: the real Snake's left arm was in fact prosthetic. Snake is thus still alive, and Junpei slowly realizes who did it. In another route, Clover makes the connection.

Heck, the entire plot is based on the idea that a person being in danger and having enough of these moments can trigger morphogenic fields, essentially allowing telepathy. Junpei gets possibly the best one, so Akane can contact him.

RuneScape: During the events leading up to the destruction of the old wizards' tower, mages were baffled on how to make new teleportation spells. The Red apprentice was working on a different problem; how to increase the effectiveness of combat spells by bypassing defenses. He had an idea he thought would work, but couldn't figure out why it wasn't. So he showed it to the Grey apprentice, who had the Eureka Moment; his idea — sending the spell through a second plane with Law magic — was the solution to the teleportation problem.

A meta example for Super Smash Bros.: Masahiro Sakurai gets swarmed with dozens of requests for characters to join the roster, and naturally, not everyone can make the cut. His solution to this? Let the players add who they want with Mii Fighters, complete with a variety of in-game costumes, three fighting styles to choose from, and twelve special attacks for each fighting style!

In Virtue's Last Reward, this happens to Sigma whenever he's in a tight situation and he suddenly, seemingly out of nowhere, gains the knowledge to overcome it. There's also a few moments where Sigma accuses a character of being the one who planted the bombs due to suddenly knowing who it was for no apparent reason. Turns out whenever he has one of these moments, he's remembering something that he found out through "mind-jumping", where he jumps into the body of alternative timeline versions of himself. It's stated in game that one of the things needed for accessing the morphogenetic field is danger, hence why it typically only happens when he's in a tight spot. Sigma himself also doesn't remember his mind-jumping: From his perspective he IS just suddenly knowing information he can't know. In order to play through these moments, the player them-self has to have gone through one of the paths where the information is revealed through one way or another, before going back and having Sigma remember that information in the path where it isn't.

Mortal Kombat 9: Throughout the game, Raiden is desperately trying to Set Right What Once Went Wrong after receiving a message from his future self during the events of Armageddon, said message being the incredibly vague "He must win." After multiple screw-ups and becoming desperate enough to try striking a deal with Quan Chi when Shao Kahn launches a full-scale invasion of Earthrealm, Raiden points out to Quan Chi that Shao Kahn can only merge the realms through victory in a Mortal Kombat tournament; otherwise, he will face the judgment of the Elder Gods. As soon as those words are out of his mouth, Raiden realizes that "He must win" actually refers to Shao Kahn himself; as his invasion is considered an unlawful breach of the rules of Mortal Kombat, Shao Kahn must be allowed to merge the realms so the Elder Gods can punish him for his violation.

A monster of some kind has planted itself outside the entrance of Xykon's lair. Xykon wants it caught alive so Redcloak can tame it. Annoyed, Redcloak complains how difficult that is, and that the last monster they had only fell asleep after eating. This inspires the two villains to defeat the beast by feeding several dozen of their own minions to it, even going as far as giving that giant crackers and celery sticks.

Elan has one after Roy suggests not to focus on Tarquin and Nale as part of his family and that he should focus on his figurative family instead. He decides to send Julio Scoundrel, whom he had met earlier.

Vaarsuvius has one when complaining about how incredibly difficult they're finding it to defeat Zzd'tri.

This is absurd! I am making the best use of my spell resources that I am able — but how in the infinite planes of existence am I supposed to be capable of defeating a wizard who has tailored not just his daily spells but his very buildspecifically to defeat... ...me.

Taito from Consolers has one when her game starts going faster as she plays. "And why does it keep going faster now? This just makes it keep getting harder and-" "Wait a minute..." The next moment, she's ready to introduce difficulty curves to the gaming world.

Web Original

In "Ayla and the Birthday Brawl" in the Whateley Universe, Phase has a Eureka Moment in the middle of the final battle of the story. It nearly turns into a Brick Joke when we don't get to hear the deduction until well into the next novel, as the attack used by the Necromancer tells Phase that there is a link between the Necromancer and Hekate, another of their Big Bads.

In Red vs. Blue episode "Test Your Might", the only way to unlock an alien AI is to pass a test of physical ability and 'mental clarity'. After Both Tucker and Agent Carolina faill, Caboose makes one of his stupid comments, prompting Church to groan, "Jesus, that empty-headed little…wait a minute. 'Empty-headed'." at that point, Church realizes that Caboose might be Too Dumb to Fool.

Western Animation

After Saying Too Much to Jeremie, Code Lyoko's fake-Franz Hopper's words give the young genius the clues to find that Franz couldn't possibly have known that "[he] was the one who let XANA destroy [Franz's] diary," flashing back to an earlier episode about it. Nice job, XANA.

In the Batman: The Animated Series, virtually every conversation Batman has with Alfred while pondering the crime du jour leads to a Eureka Moment (and an "Alfred! You're a genius!" declaration, and a bemused "Of course, sir" response).

One memorable conversation involved the Riddler and a series of riddles. Batman and Alfred are staring at the riddles and Alfred makes the comment that the riddles all involve numbers. From that, Batman turns the numbers into Roman numerals and then simultaneously, both declare, "Of course! The Department of Motor Vehicles!" (suddenly seeing the Roman numerals DMV together could easily be a Eureka Moment for any American.)

Another has Batman deducing where Count Vertigo's hideout is when Alfred tells him that he soon won't know his right hand from his left. Yes, he was confused about which direction Vertigo escaped in because his senses were scrambled, and he had actually gone in the opposite direction Batman had originally thought.

In yet another (Killer Croc's appearance on the scene in "Vendetta"), Batman realizes the nature of his foe due to Alfred's offhand comment that he was going to keep dinner in a crock pot to keep it warm.

Used on several of the earlier Sideshow Bob episodes, with "Big shoes to fill" and "Tonight on MacGyver" being two of the phrases that trigger Bart to figure out Bob's evil schemes.

Not to mention, in the episode where Sideshow Bob is the detective for once and Homer is the would-be victim, he discovers who's trying to kill Homer after Chief Wiggum mentions the work a mechanic did on the parade float. He then flashes back to the wrench that was used to prevent Homer from escaping a sauna and the oil fingerprint on the invitation letter to said sauna, as well as the mechanic that he and Homer had met earlier.

In one flashback episode, several people congratulated Homer because Marge had become pregnant (with Maggie). Homer, himself unaware of the pregnancy, misinterpreted these comments (even the ridiculously direct ones) as regarding his new job. Then one character congratulates him on the new job, prompting Homer to respond, "New job? MARGE IS PREGNANT!?" That's "ridiculously direct", as in "Hey, Homer, way to get Marge pregnant!" "This is getting increasingly abstract, but yes, I do enjoy working at the bowling alley"

When the family is trying to figure out a way to keep Apu from being deported, Abe mentions he could try living in a balloon. Lisa exclaims "That's it!", leading Bart to declare that she's as dumb as him. She explains that she connects Abe being a grandfather with grandfather clause, with his statement being irrelevant.

Captain Flamingo runs on this trope. Every use of the eponymous character's "Bird Brain" is either this, or a full-on I Was Just Joking, depending on which would be funnier. Either way, it's played for laughs, as the ideas he gets are usually ridiculous... but always manage to work.

According to Animaniacs, Albert Einstein has conceived his famous mass/energy equivalence formula (you know, E=mc^2) while watching Wakko writing "Acme" backwards (his "a" looked like a "2"). In a similar episode, the Warners were cleaning Beethoven's chimney (badly, of course) and humming an obnoxious tune that went a little something like "Hm hm hm hmmmmmmmm". As they're leaving, ol' Ludwig finally has the inspiration for his Fifth Symphony. The next house on the Warners' route is "that Van Gogh grouch again", and Wakko picks a sunflower to help cheer him up.

In an episode of The Raccoons, Cyril is accused of stealing a gem during a blackout. Bert is trying to solve the crime but is stumped until he sees Cedric drop his Opaque Nerd Glasses in the river. It's then that he realizes that the gem was not stolen but knocked in an aquarium, and was rendered invisible by water refraction, same as Cedric's lenses.

The Adventures of Jimmy Neutron: Boy Genius had a recurring delayed reaction to this. When the heroes have exhausted all their obvious options, Jimmy starts thinking about the episode's events. One completely ordinary-seeming event would pop into his mind, he'd shout "Brain Blast!", and he'd come up with a solution based on that event.

Spoofed in an episode of Johnny Bravo where Johnny's enlisted the help of Adam West to find his missing Momma. They stop for lunch at a Chinese restaurant and West interprets his fortune cookie message ("Your heart's afire"), via Batmanlogic, to mean that Momma Bravo's being held prisoner at the golf course.

Sent up in a Running Gag in the episode "Cancelled". The astronomer investigating Cartman's satellite dish implant draws several correct conclusions after increasingly absurd free association sessions based on conversations with Chef.

Mr. Garrison struggled to invent a new vehicle until Mr. Hat commented "Boy, that Enrique Iglesias can sure gyrate his hot ass around" and decided on a gyroscope.

Shego's mockery of her evil employer Dr. Drakken in Kim Possible often gives him inspiration for his next World Domination plot, such as when he decides to go on the offensive against Kim Possible.

When Kim visited her cousin Larry, he commented that Monty Fiske, the archeologist they had assisted earlier, was a master of Tai Shing Pek Kwar or Monkey Kung-Fu, prompting Kim to realize that he was the villain Monkey Fist.

Farnsworth: Amy, technology isn't intrinsically good or evil. It's how it's used. Like the Death Ray. Amy: Maybe you're right. I guess science has to keep pushing forward, with the hope that... That's it! Pushing forward. Professor, I know how to restart the Earth! Farnsworth: Pssh. You can't suddenly know something by assembling a committee of words... That's it! I'll assemble your committee!

In Kung Fu Panda, Po opens the scroll containing the secret to limitless power and kung fu itself to find nothing but a blank, reflective foil, which seems to imply that obtaining limitless power is impossible. He then meets his father who says that the secret ingredient to his popular "Secret Ingredient Soup" is also nothing; it's special because people believe it is. This leads Po to having his Eureka Moment: that limitless power resides within oneself (hence the reflection), and that "there is no secret ingredient".

Finn from Adventure Time has one in which the word "RENCE" on one half of a murder weapon makes him think of Clarence, whom he had met several minutes prior.

In "Apple Thief", Finn solves a case when he's tipped off by the sentence, "This place could use a scarecrow."

Terrytoons' TV character Tom Terrific will usually get a Eureka Moment when Mighty Manfred the Wonder Dog says something off the cuff to try to weasel out of a situation. In "Go West, Young Manfred," Tom is looking for a way to get back to the settler with his cap full of gold:

In The Powerpuff Girls episode "Mommy Fearest", after the girls are grounded by the Professor's new wife Ima Goodlady, Blossom gets a call from the Mayor saying that Sedusa is robbing him of his jewels. There, Blossom puts the pieces together about this coincidence and deduces that the two of them are one and the same and it was all part of Sedusa's scheme to keep them away while she committed crime.

A minor example: in the Steven Universe episode "Log Date 7 15 2", Peridot spends much of the episode trying to understand why Garnet enjoys being fused all the time. She ultimately figures it out when it's put in the terms of her favorite Earth TV show:

Garnet: I'm Percy and Pierre.

Peridot: ...oooooh!!!

Real Life

The word "Eureka" originates from ancient Greek, meaning "I have found it!" Archimedes was consulted to figure out how to tell whether a crown that the king had commissioned was made from the pure gold he had supplied to the jeweler, or whether the jeweler had substituted silver for gold to make a crown the same weight. But Archimedes couldn't damage the crown in any way to do so, and as the crown was such an odd shape, he was unable to math it out. When Archimedes took a bath, some of the bathwater overflowed the edge of the tub, prompting him to realize that an object displaces its equal volume in water. Jumping out of the water, Archimedes shouted "Eureka!" and ran to report this discovery to the king. Naked. The subject of volume displacement in physics is, fittingly enough, known as "Archimedes' Law" because of this. (A Ted Talk presents an alternate theory that the project was building a massive ship, as "crown" and "keel" sound similar in Greek. See the video.)

Just in general, this is Truth in Television. It's been proven that people are more likely to reach an answer they can't think of by not thinking about it directly. Typically happens when you've forgotten something, when you're trying to think of an answer to some hard crossword, or something else mundane. If you're really struggling to think of it, then sitting back and thinking of other seemingly unrelated things has been shown to result in what you were looking for bubbling up.

Sometimes referred to as the "Toilet Moment" or the "Bed Eureka", due to this typically happening to people when they're on the toilet or trying to sleep. The reason being that people typically don't have anything to do when doing either of these things so their mind wanders, and somehow finds an answer to something or some sort of inspiration.

Newton's understanding of gravity supposedly came after an apple fell on his head. (Which never actually happened, but nobody cares about that.)

The accepted explanation is usually that he came up with the law while thinking about apples falling from trees (or perhaps even saw an apple fall to the ground), but the story about one actually falling on his head is just fluff. Newton himself told this version later in life.

A similar tale surrounds the invention of the sewing machine: the inventor dreamed of spears with holes in them stabbing towards him, and realized upon waking that the eye of a needle to fit into a sewing machine had to be in the tip.

Supposedly, Eli Whitney came about the idea of the cotton gin by watching a cat wash itself.

According to IMDB, composer Bill Conti had a rocking theme all ready for the Training Montage, but couldn't figure out what to call it. Director Avildsen, impressed by the nameless piece, agreed that "It should be almost like Rockyis flying now."

Watson and Crick, co-discoverers of the DNA molecule's double-helix structure, got the idea after noticing a spiral staircase. It was a completely unlikely solution based on the limited evidence.

The inventor of Genetic Fingerprinting, the DNA identifying technique used by forensic investigators and dramas all over the world, Professor Sir Alec Jeffreys, had such a moment (and it is frequently described as a Eureka Moment) while looking at an X-ray film image of a DNA experiment at the University of Leicester. Noticing the obvious similarities and differences between the DNA of family members, within half an hour he saw the potential.

Parodied by Discworld, by suggesting that DNA might have been faster but only licensed to carry 14 people, if he'd been looking at an elevator during the Eureka moment.

Gauss once wrote in his diary "EYPHKAnote Those are actually the Greek letters epsilon-upsilon-rho-eta-kappa-alpha, transliterated as E-U-R-E-K-A! num = Δ + Δ + Δ," thinking he'd proven Fermat's famously unproven polygonal number conjecture (yes, that's right, he did it more than once) for n = 3; he later realized that the proof in his head needed significant ironing out, but for an open question, he got it quickly enough.

According to Cognitive Psychology, when it comes to problem solving those "Eureka Moments" are actually called insights which are deep, useful understandings of the nature of a problem. However, compared to the typical slow approach to a problem solution, insights often occur abruptly and almost without warning. Tasks that involve insight usually require something new and non-obvious to be done and in most cases they are difficult enough to predict that the initial solution attempt will be unsuccessful. This can lead to the so called "AHA-experience" where the solution pops up all of a sudden.

Merv Griffin came up with the name of his popular quiz show format Jeopardy! after a network exec told him that the show, piloted under the name That's the Question, needed "more jeopardies".

In the late 90's, a few sitcom producers came up with pilots for the Fox Network. The most promising one was about a group of teenagers growing up in The '70s. But there was a problem: their choices for titles all had possible legal issues. After a test screening, one member of the survey group gave them their title by saying "I loved That '70s Show."

After people started writing apps which made phone screens bright white so they could be used as flashlights, someone realized: "Wait, you know the camera flash? Why don't we just give it an on-switch?", and a much more practical flashlight app was born.

Bob Gale got the idea for Back to the Future when he visited his parents and looked through his father's high school yearbook, learning his father had been the class president. Remembering his own high school class president, who was somebody he didn't care for, Gale wondered if he would've been friends with his father had they gone to high school together.

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